General forms of the Menshov-Rademacher, Orlicz, and Tandori theorems on orthogonal series

Details General forms of the Menshov-Rademacher, Orlicz, and Tandori theorems on orthogonal series General forms of the Menshov-Rademacher, Orlicz, and Tandori theorems on orthogonal series

2011-10-19

arxiv.org/abs/1110.4253v2

Methods Funct. Anal. Topology 17 (2011), no. 4, 330-340

Mathematics

Functional Analysis

in English, translation of the 1-st (Russian) version, 12 pages

Scientific paper

We prove that the classical Menshov-Rademacher, Orlicz, and Tandori theorems remain true for orthogonal series given in the direct integrals of measurable collections of Hilbert spaces. In particular, these theorems are true for the spaces L_{2}(X,d\mu;H) of vector-valued functions, where (X,\mu) is an arbitrary measure space, and H is a real or complex Hilbert space of an arbitrary dimension.

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